Given an integer **N** which represents the number of Vertices. The Task is to find the maximum number of edges possible in a Bipartite graph of **N** vertices.**Bipartite Graph:**

- A Bipartite graph is one which is having 2 sets of vertices.
- The set are such that the vertices in the same set will never share an edge between them.

**Examples:**

Input:N = 10Output:25

Both the sets will contain 5 vertices and every vertex of first set

will have an edge to every other vertex of the second set

i.e. total edges = 5 * 5 = 25Input:N = 9Output:20

**Approach:** The number of edges will be maximum when every vertex of a given set has an edge to every other vertex of the other set i.e. **edges = m * n** where **m** and **n** are the number of edges in both the sets. in order to maximize the number of edges, **m** must be equal to or as close to **n** as possible. Hence, the maximum number of edges can be calculated with the formula,

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to return the maximum number` `// of edges possible in a Bipartite` `// graph with N vertices` `int` `maxEdges(` `int` `N)` `{` ` ` `int` `edges = 0;` ` ` `edges = ` `floor` `((N * N) / 4);` ` ` `return` `edges;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `N = 5;` ` ` `cout << maxEdges(N);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `class` `GFG {` ` ` `// Function to return the maximum number` ` ` `// of edges possible in a Bipartite` ` ` `// graph with N vertices` ` ` `public` `static` `double` `maxEdges(` `double` `N)` ` ` `{` ` ` `double` `edges = ` `0` `;` ` ` `edges = Math.floor((N * N) / ` `4` `);` ` ` `return` `edges;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `double` `N = ` `5` `;` ` ` `System.out.println(maxEdges(N));` ` ` `}` `}` `// This code is contributed by Naman_Garg.` |

## Python3

`# Python3 implementation of the approach` `# Function to return the maximum number` `# of edges possible in a Bipartite` `# graph with N vertices` `def` `maxEdges(N) :` ` ` `edges ` `=` `0` `;` ` ` `edges ` `=` `(N ` `*` `N) ` `/` `/` `4` `;` ` ` `return` `edges;` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` ` ` `N ` `=` `5` `;` ` ` `print` `(maxEdges(N));` `# This code is contributed by AnkitRai01` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG {` ` ` `// Function to return the maximum number` ` ` `// of edges possible in a Bipartite` ` ` `// graph with N vertices` ` ` `static` `double` `maxEdges(` `double` `N)` ` ` `{` ` ` `double` `edges = 0;` ` ` `edges = Math.Floor((N * N) / 4);` ` ` `return` `edges;` ` ` `}` ` ` `// Driver code` ` ` `static` `public` `void` `Main()` ` ` `{` ` ` `double` `N = 5;` ` ` `Console.WriteLine(maxEdges(N));` ` ` `}` `}` `// This code is contributed by jit_t.` |

## PHP

`<?php` `// PHP implementation of the approach` `// Function to return the maximum number` `// of edges possible in a Bipartite` `// graph with N vertices` `function` `maxEdges(` `$N` `)` `{` ` ` `$edges` `= 0;` ` ` `$edges` `= ` `floor` `((` `$N` `* ` `$N` `) / 4);` ` ` `return` `$edges` `;` `}` `// Driver code` ` ` `$N` `= 5;` ` ` `echo` `maxEdges(` `$N` `);` `// This code is contributed by ajit.` `?>` |

## Javascript

`<script>` `// Javascript implementation of the approach` `// Function to return the maximum number` `// of edges possible in a Bipartite` `// graph with N vertices` `function` `maxEdges(N)` `{` ` ` `var` `edges = 0;` ` ` `edges = Math.floor((N * N) / 4);` ` ` `return` `edges;` `}` `// Driver code` `var` `N = 5;` `document.write( maxEdges(N));` `</script>` |

**Output:**

6

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